Abelianp-groups determined by their Ulm sequences
Peter Crawley · Pacific Journal of Mathematics · 1967
Ulm's theorem asserts that, within the class of all reduced countable abelian p-groups, a group is determined, up to isomorphism, by its Ulm sequence.Although this theorem fails in general for uncountable groups, there are classes of uncountable abelian p-groups whose members are determined within the class by their Ulm sequences.Eolettis has shown that the class of direct sums of countable p-groups has this property.Here it is shown that the class of those abelian p-groups for which the Ulm type is finite and all the Ulm factors except the last are direct sums of cyclic groups, is another such class.